Question:medium

Two numbers are in the ratio 8 : 11 and their LCM is 2816. What would be the difference between the two numbers?

Updated On: Jun 30, 2026
  • 64
  • 72
  • 84
  • 96
  • 256
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The Correct Option is D

Solution and Explanation

The correct answer is option (D):
96

Let's break down how to solve this problem step-by-step.

We are given that two numbers are in the ratio 8:11. This means we can represent the numbers as 8x and 11x, where x is a common factor.

We are also given that the least common multiple (LCM) of these two numbers is 2816. The LCM is the smallest number that both numbers divide into evenly.

To find the LCM of 8x and 11x, we first find the LCM of 8 and 11. Since 8 and 11 have no common factors other than 1, their LCM is simply their product: 8 * 11 = 88.

Now, because the numbers are 8x and 11x, the LCM of the numbers themselves is the LCM of the coefficients (8 and 11), multiplied by x. Therefore, the LCM of 8x and 11x is 88x.

We know the LCM is 2816, so we can set up the equation:

88x = 2816

To solve for x, divide both sides of the equation by 88:

x = 2816 / 88
x = 32

Now that we know the value of x, we can find the two numbers:

* 8x = 8 * 32 = 256
* 11x = 11 * 32 = 352

Finally, to find the difference between the two numbers, subtract the smaller number from the larger number:

352 - 256 = 96

Therefore, the difference between the two numbers is 96.
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